In recent years, an RGB coupler module using a silica-based planar lightwave circuit (PLC) has been drawing attention as a circuit element that multiplexes visible light beams of three primary colors for eyeglass-type devices and projectors (see Non Patent Literature 1, for example). In the PLC, optical waveguides are created in a planar substrate by patterning and etching processes in photolithography or the like and a plurality of basic optical circuits (e.g. directional couplers, Mach-Zehnder interferometers, etc.) are combined with each other to implement various functions.
There is a three-primary-color multiplexing circuit that utilizes, for example, directional couplers and/or Mach-Zehnder interferometers (see Non Patent Literature 1). In this description, the simplest case of using directional couplers will be described by taking FIG. 1 as an example.
FIG. 1 illustrates the basic structure of an RGB coupler module using a PLC. As illustrated in FIG. 1, the basic structure of the RGB coupler module using a PLC is formed of three optical waveguides, which are first to third optical waveguides 1 to 3. A first directional coupler 4 is coupled to the first optical waveguide 1. An output waveguide 5 is coupled to the second optical waveguide 2. A second directional coupler 6 is coupled to the third optical waveguide 3. The waveguide length, waveguide width, and inter-waveguide gap of the first directional coupler 4 are designed such that the first directional coupler 4 couples a light beam with a wavelength λ1 from the first optical waveguide 1 to the second optical waveguide 2, and couples a light beam with a wavelength λ2 from the second optical waveguide 2 to the first optical waveguide 1 and from the first optical waveguide 1 to the second optical waveguide 2. The waveguide length, waveguide width, and inter-waveguide gap of the second directional coupler 6 are designed such that the second directional coupler 6 couples a light beam with a wavelength λ3 from the third optical waveguide 3 to the second optical waveguide 2 and transmits the light beams with the wavelength λ1 and the wavelength λ2.
In one example where λ1<λ2<λ3, a blue light beam (wavelength λ1) is input to the first optical waveguide 1, a green light beam (wavelength λ2) is input to the second optical waveguide 2, and a red light beam (wavelength λ3) is input to the third optical waveguide 3, for example. The light beams of the three colors are multiplexed through the first directional coupler 4 and the second directional coupler 6 and output from the output waveguide 5. Unlike an optical multiplexing circuit for communication with a small bandwidth ratio, a three-primary-color optical multiplexing circuit deals with the wavelength of the blue light beam (wavelength band 400 nm) and the wavelength of the red light beam (wavelength band 700 nm), which greatly differ from each other. Accordingly, the wavelength dependency of the coupling length is significant. This makes it possible to make a configuration as above.
Also, as discussed in Non Patent Literature 2, light beams with different wavelengths can be multiplexed also by using a multi-mode interference (MMI) waveguide. However, since each of the number of input waveguides and the number of output waveguides is two, it is difficult to multiplex light beams with three or more wavelengths by using MMI.
A directional coupler will be briefly described below for the understanding of the embodiments of the present invention to be described later. FIG. 2 illustrates the basic principle of a directional coupler. FIG. 2 illustrates two waveguides 11 and 12. As illustrated in FIG. 2, the directional coupler is a coupler that transfers a light beam passing through one of the waveguides, or the waveguide 11, to the opposite waveguide 12 in a state where the two waveguides 11 and 12 are arranged close to each other.
Let a z axis be set along the light travel direction. Then, in a case where a light beam with a light intensity of 1 is input to the waveguide 11, the light intensity of the light beams propagating through the waveguide 11 and the waveguide 12 is P1(z) and P2(z) at a position Z, respectively. q=κ2+δ2, F=1/(1+(δ/κ)2), and δ=(β2−β1)/2 are given, where κ is the mode coupling constant, and β1 and β2 are the propagation constants of the waveguide 11 and the waveguide 12, respectively. P1(z) and P2(z) are expressed by (equation 1) and (equation 2) below, respectively.P1(z)=1−F sin2(qz)  (Equation 1)P2(z)=F sin2(qz)  (Equation 2)
Here, the ratio of transfer of the light beam from the waveguide 11 to the waveguide 12 is greatest when z=π/2q·(2m+1), where m=0, 1, 2, . . . . The distance when m=0 is called the coupling length. Also, when δ=0, the light transfer ratio is 100%.